Sagnac effect is a phase shift induced in a wave propagating in a loop by rotation of the loop. Two waves propagating in opposite directions along a rotating closed loop may interfere in a point of exit, wherein the rotation may cause a phase shift between them. An optical Sagnac Interferometer apparatus may include, for example, a loop trajectory enclosing an area. The interferometer may operate by splitting a beam of light at an entrance of the loop, to two beams which may be made to propagate in opposite directions along the loop trajectory. An interference pattern may be obtained at a point of exit from the loop. When the apparatus rotates, the path length of one of the beams may be effectively shortened, while the path length of the other beam may be effectively lengthened. Therefore, a phase shift may be created between the two beams, dependent on the rotation velocity of the apparatus.
Therefore, a Sagnac interferometer may measure changes in the rotation frequency of the frame that it is fixed to, relative to a global (inertial) frame of reference. The Sagnac effect in a wave propagating through a closed rotating ring induces a phase shift proportional to the rotation frequency Ω of this rotation and the area A of the ring. For light waves with frequency ω this phase shift may be represented by Φlight=(2ωA/c2)Ω, where c is the speed of light and ω is the light frequency. For matter waves of massive particles with mass m, the induced phase shift may be represented by Φmatter=(2mA/ℏ)Ω, which is larger than the phase shift in an optical SI having the same area A by mc2/ℏω, wherein ℏ is plank's constant. Therefore, the Sagnac phase is much more sensitive to rotations in a matter-wave SI compared to light wave SI, for example, by 10 orders of magnitude. However, state-of-the-art matter-wave Sagnac interferometers, which are based on beams of atoms traveling in free space, are limited by their area, number of atoms and the allowed momentum bandwidth of the atoms.
It will be appreciated that for simplicity and clarity of illustration, elements shown in the figures have not necessarily been drawn to scale. For example, the dimensions of some of the elements may be exaggerated relative to other elements for clarity. Further, where considered appropriate, reference numerals may be repeated among the figures to indicate corresponding or analogous elements.